Bounds on Lyapunov Exponents via Entropy Accumulation


METADATA ONLY
Loading...

Date

2021-01-01

Publication Type

Journal Article

ETH Bibliography

yes

Citations

Altmetric
METADATA ONLY

Data

Rights / License

Abstract

Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an information theoretic tool called entropy accumulation theorem we derive an upper and a lower bound for the maximal and minimal Lyapunov exponent, respectively. The bounds assume independence of the random matrices, are analytical, and are tight in the commutative case as well as in other scenarios. They can be expressed in terms of an optimization problem that only involves single matrices rather than large products. The upper bound for the maximal Lyapunov exponent can be evaluated efficiently via the theory of convex optimization.

Publication status

published

Editor

Book title

Volume

67 (1)

Pages / Article No.

10 - 24

Publisher

IEEE

Event

Edition / version

Methods

Software

Geographic location

Date collected

Date created

Subject

Lyapunov exponent; random matrices; quantum entropy; convex optimization

Organisational unit

03781 - Renner, Renato / Renner, Renato check_circle

Notes

Funding

165843 - Fully quantum thermodynamics of finite-size systems (SNF)

Related publications and datasets

Is new version of: